3) For known k ≥ 2 show that the negative binomial distribution with probability mass function, f(y, k, p) = = y = 0, 1, 2,.. 1 k k k (¹ + k − ¹) (¹ - 4 k)" (₁² k) ^ 1 Y u + + 1 belongs to the exponential family of distributions. Find the natural parameter for this distribution.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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3) For known k ≥ 2 show that the negative binomial distribution with probability mass
function,
f(y, k, μ)
y = 0, 1, 2, ..
=
- 1
k
k
k
(³ + k − ¹) (¹ − µ 4 k)" (1² k) "
1
Y
+
1
belongs to the exponential family of distributions. Find the natural parameter for this
distribution.
Transcribed Image Text:3) For known k ≥ 2 show that the negative binomial distribution with probability mass function, f(y, k, μ) y = 0, 1, 2, .. = - 1 k k k (³ + k − ¹) (¹ − µ 4 k)" (1² k) " 1 Y + 1 belongs to the exponential family of distributions. Find the natural parameter for this distribution.
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